Question

A store sells almonds for $7 per pound, cashews for $10 per pound, and walnuts for $12 per pound. A customer buys 12 pounds of mixed nuts consisting of almonds, cashews, and walnuts for $118. The customer buys 2 more pounds of walnuts than cashews. The matrix below represents this situation.
mc020-1.jpg

a. The customer buys 1 more pound of walnuts than almonds and 1 more pound of almonds than cashews.

b. The customer buys 2 more pounds of walnuts than almonds and 2 more pounds of almonds than cashews.

c. The customer buys 0.5 more pound of walnuts than almonds and 2.5 more pounds of almonds than cashews.

d. The customer buys 6.5 more pounds of walnuts than almonds and 8.5 more pounds of almonds than cashews.

Answer 1

The complete question in the attached figure

Let
x------------->  pounds of almonds-------> ($7 per pound)
y------------->  pounds of cashews-------> ($10 per pound)
z------------->  pounds of walnuts------->  ($12 per pound)

we know that
x+y+z=12---------------> equation 1
7x+10y+12z=118---------> equation 2
z=2+y--------------------> equation 3

replacing equation 3 in 1 and 2
x+y+(2+y)=12----------> x+2y=10--------> equation 4
7x+10y+12*(2+y)=118--> 7x+10y+24+12y=118--> 7x+22y=94 --> equation 5

using a graph tool-----> to resolve the system of equations
see the attached figure

the solution is the point (4,3)
x=4
y=3
z=2+y-----> z=2+3-------->z=5

pounds of almonds are 4
pounds of cashews are 3
pounds of walnuts are 5

therefore

the answer is the option
a. The customer buys 1 more pound of walnuts than almonds and 1 more pound of almonds than cashews